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BAGHDAD (AP) -- For nearly two years, U.S. airstrikes, military advisers and weapons shipments have helped Iraqi forces roll back the Islamic State group. The U.S.-led coalition has carried out more than 5,000 airstrikes against IS targets in Iraq at a total cost of $7 billion since August 2014, including operations in Syria. On Tuesday a U.S. Navy SEAL was the third serviceman to die fighting IS in Iraq.

But many Iraqis still aren't convinced the Americans are on their side.

Government-allied Shiite militiamen on the front-lines post videos of U.S. supplies purportedly seized from IS militants or found in areas liberated from the extremist group. Newspapers and TV networks repeat conspiracy theories that the U.S. created the jihadi group to sow chaos in the region in order to seize its oil.

Despite spending more than $10 million on public outreach in Iraq last year, the U.S. government appears to have made little headway in dispelling such rumors. An unscientific survey by the State Department of Iraqi residents last year found that 40 percent believe that U.S. policy is working to "destabilize Iraq and control its natural resources," and a third believe America "supports terrorism in general and (IS) specifically."

Skepticism about U.S. motives is deeply rooted in Iraq, where many still blame the chaos after the 2003 invasion that toppled Saddam Hussein on American malice rather than incompetence. The conspiracy theories are also stoked by neighboring Iran, which backs powerful militias and political parties with active media operations.

Among the most vocal critics is al-Ahad TV - a 24-hour satellite channel funded by Asaib Ahl al-Haq, an Iranian-backed militia allied with the Iraqi government. The channel airs front-line reports and political talk shows where the allegedly harmful role of the U.S. government frequently comes up.

The U.S. "aims at weakening Iraq and the Arab world as well as the Shiites," al-Ahad's spokesman Atheer al-Tariq said. "They spare no efforts to destabilize Iraq and neighboring countries in order to continue selling weapons and strengthening their presence in the region through establishing more military bases," he added.

While supervising the channel's war reporting last year, he claimed to have witnessed incidents when U.S. forces helped IS. As Iraqi security forces prepared to enter the city of Tikrit in April, he said two U.S. helicopters evacuated senior militants. A few months later, during an operation to retake the Beiji oil refinery, crates of weapons, ammunition and food were dropped over militant-held territory, he said.

"Is it logical to believe that America, the source of technology and science, could fire a rocket or drop aid materials in a mistaken way?" he asked.

Videos uploaded to social media by front-line militiamen purport to tell a similar story. One shows U.S. military MREs, "meals, ready-to-eat," as well as uniforms and weapons said to have been found in an area held by IS. Another shows the interrogation of a captured IS militant. "Check out his boots, they are from the U.S. army," a fighter says. Another fighter points to a pile of rocket-propelled grenades he says were made in the U.S. and shipped to IS.

There are more plausible explanations for U.S. supplies being found in the hands of the extremists.

When IS swept across northern and western Iraq in the summer of 2014 it captured armored vehicles, heavy weapons and other U.S. equipment that had been provided to Iraqi security forces at a cost of billions of dollars. And despite the U.S. military's technical sophistication, it's not unheard of for airdrops or strikes to miss their mark in the heat of battle.

The U.S. Embassy and the U.S.-led coalition have invested considerable time and resources in refuting the allegations.

Both run Twitter feeds, Facebook pages and hold regular press conferences, and U.S. officials frequently appear as guests on Iraqi TV networks. With a budget of $10.67 million for the 2015 fiscal year, the public diplomacy section for Iraq is the third largest in the world, according to a 2015 report by the State Department's Special Inspector General.

"There are a lot of players out here on this information and media battle space," said U.S. Army Col. Steve Warren, the spokesman for the U.S.-led coalition.

"The Iranians have something to say every day, the Russian have something to say every day, ISIL has something to say every single day, so we need to make sure that this coalition and this Iraqi government is also saying something every day," he said, using an alternative acronym for IS.

"This coalition is here to fight ISIL," he said, "not provide them MREs."

But if there is a media war underway, the U.S. appears to be losing it. In December 2014, 38 percent of Iraqis had a favorable view of the U.S., but by August 2015 that had dropped to just 18 percent, according to the State Department's unscientific survey.

A group of Iraqi men smoking cigarettes and sipping tea outside a Baghdad shop selling books and newspapers said their skepticism extends beyond U.S. officials. They say Iraqis are well aware that most media outlets are run by political parties furthering their own agendas.

"Iraqi media isn't professional, it's all just ideology," Abu Muhammed said, asking that his full name not be used for fear of reprisals.

But he said the accusations of U.S. support for IS are hard to ignore because of America's confusing tangle of regional alliances. "The U.S. is always fighting groups on one side that they also support on the other side," he said. He pointed to Syria, where the U.S. supports Syrian Kurdish fighters who are considered terrorists by NATO ally Turkey.

Others simply can't understand how the world's most powerful military hasn't been able to defeat the extremists.

"They took out Saddam in two weeks, but they can't finish IS in two years?" asked Falih, another Iraqi who asked that his last name not be used out of security concerns. "It just doesn't make sense."